What is a Function Notation

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What does "Function Notation" mean?

The function notation is a simple and efficient way to write functions, making them easy to write, understand, and evaluate. It uses algebraic expressions to summarize how a function affects the input value to get the desired output value. The relationship between the input and output values is shown by the function $f(x)$ , read as " $f$ of $x$ ".

How do you evaluate the values of a function notation?

When evaluating function notations for a specific input value, substitute the input value into the algebraic expression that defines the function. When figuring out the value of a function notation, the focus is on one input and the output that goes with it.

Look at the function shown above. When evaluating $f(x) \ = \ 2x \ + \ 7$ at $x \ = \ 9$ , substitute the given input value to evaluate and find the value of $f(9)$ .
$f(x) \ = \ 2(9) \ + \ 7 \ = \ 18 \ + \ 7 \ = \ 25$

Function Notation

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Exercises for Function Notation

1) $p(s) = 4s \ + \ 2$ , find $p(8)$ $\ \Rightarrow \$

2) $f(x) = 6x^2 \ + \ x \ + \ 2$ , find $f(2)$ $\ \Rightarrow \$

3) $f(x) = 11x^2 \ - \ x \ + \ 2$ , find $f(4)$ $\ \Rightarrow \$

4) $g(t) = 2t^2 \ + \ 3$ , find $g(9)$ $\ \Rightarrow \$

5) $p(s) = 9s^2 \ + \ 4$ , find $p(3)$ $\ \Rightarrow \$

6) $m(u) = 10u^2 \ + \ 2$ , find $m(6)$ $\ \Rightarrow \$

7) $p(s) = 4s^2 \ - \ s \ + \ 9$ , find $p(9)$ $\ \Rightarrow \$

8) $g(t) = 7t^2 \ + \ t \ + \ 7$ , find $g(6)$ $\ \Rightarrow \$

9) $m(u) = 5u \ + \ 3$ , find $m(2)$ $\ \Rightarrow \$

10) $f(x) = 6x \ + \ 7$ , find $f(8)$ $\ \Rightarrow \$

Answers

$p(s) = 4s \ + \ 2$ , find

$p(8)$

$\ \Rightarrow \ \color{red}{p(8) = 34}$

Solution
Substitute

$8$ for (s) and solve it:

$p(8) = 4(8) + 2 = 4 \times 8 + 2 = 32 + 2 = 34$

$f(x) = 6x^2 \ + \ x \ + \ 2$ , find

$f(2)$

$\ \Rightarrow \ \color{red}{f(2) = 28}$

Solution
Substitute \2\ for (x) and solve it:

$f(2) = 6 \times 2 ^2 + 2 + 2 = 28$

$f(x) = 11x^2 \ - \ x \ + \ 2$ , find

$f(4)$

$\ \Rightarrow \ \color{red}{f(4) = 174}$

Solution
Substitute \4\ for (x) and solve it:

$f(4) = 11 \times 4 ^2 - 4 + 2 = 174$

$g(t) = 2t^2 \ + \ 3$ , find

$g(9)$

$\ \Rightarrow \ \color{red}{g(9) = 165}$

$p(s) = 9s^2 \ + \ 4$ , find

$p(3)$

$\ \Rightarrow \ \color{red}{p(3) = 85}$

$m(u) = 10u^2 \ + \ 2$ , find

$m(6)$

$\ \Rightarrow \ \color{red}{m(6) = 362}$

$p(s) = 4s^2 \ - \ s \ + \ 9$ , find

$p(9)$

$\ \Rightarrow \ \color{red}{p(9) = 324}$

$g(t) = 7t^2 \ + \ t \ + \ 7$ , find

$g(6)$

$\ \Rightarrow \ \color{red}{g(6) = 265}$

$m(u) = 5u \ + \ 3$ , find

$m(2)$

$\ \Rightarrow \ \color{red}{m(2) = 13}$

10)

$f(x) = 6x \ + \ 7$ , find

$f(8)$

$\ \Rightarrow \ \color{red}{f(8) = 55}$

What is a Function Notation